Problem: Kevin is 5 times as old as Michael. Four years ago, Kevin was 7 times as old as Michael. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Michael. Let Kevin's current age be $k$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $k = 5m$ Four years ago, Kevin was $k - 4$ years old, and Michael was $m - 4$ years old. The information in the second sentence can be expressed in the following equation: $k - 4 = 7(m - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = k / 5$ . Substituting this into our second equation, we get: $k - 4 = 7($ $(k / 5)$ $- 4)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 4 = \dfrac{7}{5} k - 28$ Solving for $k$ , we get: $\dfrac{2}{5} k = 24$ $k = \dfrac{5}{2} \cdot 24 = 60$.